Solve (2-b)(1+2b)+(1+b)(b^3-3b)

$$( 2 - b ) ( 1 + 2 b ) + ( 1 + b ) ( b ^ { 3 } - 3 b )$$

Evaluate

$$b^{4}+b^{3}-5b^{2}+2$$

Solution Steps

Use the distributive property to multiply 2-b by 1+2b and combine like terms.

$$2+3b-2b^{2}+\left(1+b\right)\left(b^{3}-3b\right)$$

Use the distributive property to multiply 1+b by b^{3}-3b.

$$2+3b-2b^{2}+b^{3}-3b+b^{4}-3b^{2}$$

Combine 3b and -3b to get 0.

$$2-2b^{2}+b^{3}+b^{4}-3b^{2}$$

Combine -2b^{2} and -3b^{2} to get -5b^{2}.

$$2-5b^{2}+b^{3}+b^{4}$$

Expand

$$b^{4}+b^{3}-5b^{2}+2$$

Solution Steps

Use the distributive property to multiply 2-b by 1+2b and combine like terms.

$$2+3b-2b^{2}+\left(1+b\right)\left(b^{3}-3b\right)$$

Use the distributive property to multiply 1+b by b^{3}-3b.

$$2+3b-2b^{2}+b^{3}-3b+b^{4}-3b^{2}$$

Combine 3b and -3b to get 0.

$$2-2b^{2}+b^{3}+b^{4}-3b^{2}$$

Combine -2b^{2} and -3b^{2} to get -5b^{2}.

$$2-5b^{2}+b^{3}+b^{4}$$